A microwave oven operates at 2.70 ghz . what is the wavelength of the radiation produced by this appliance? express the wavelength numerically in nanometers.

Microwaves are electromagnetic radiations, and they travel at the speed of light:
[tex]c=3 \cdot 10^8 m/s[/tex].
The relationship between wavelength and frequency of a wave is given by:
[tex]c= \lambda f[/tex],
where [tex] \lambda [/tex] is the wavelength and f the frequency. For the microwaves in this problem, the frequency is
[tex]f=2.70 GHz=2.7\cdot 10^9 Hz[/tex]
therefore we can find their wavelength by rearranging the above equation and plugging these data into it:
[tex]\lambda= \frac{c}{f}= \frac{3\cdot 10^8 m/s}{2.7 \cdot 10^9 Hz}=0.11 m[/tex]
which corresponds to [tex]\lambda= 1.1 \cdot 10^8 nm[/tex].

avantikar avantikar · Answer 2 · 2019-09-04T10:49:35+02:00

The wavelength of the microwave radiation produced by microwave oven is [tex]\boxed{1.1\times {10^8}\,{\text{nm}}}[/tex].

Further Explanation:

A microwave is an appliance which is used to heat and cook food by direct exposing it to electromagnetic radiation. Microwave oven uses radio waves to heat and cook food. A magnetron is used as a source of microwave radiation.

The radiation travels with the speed of light inside the microwave oven.

Given:

The operational frequency of the microwave oven is [tex]2.70\text{ GHz}[/tex].

The speed of the radiation is [tex]3\times10^{8}\text{ m/s}[/tex].

Concept:

The frequency and wavelength of an electromagnetic radiation are related according to the following expression.

[tex]c=f \cdot \,\lambda[/tex]

Rearrange the above expression for [tex]\lambda[/tex] .

[tex]\boxed{\lambda=\dfrac{c}{f}}[/tex] …… (1)

Here, [tex]c[/tex] is the speed of light, [tex]f[/tex] is the frequency of the radiation and [tex]\lambda[/tex] is the wavelength of the radiation.

Converting [tex]\text{GHz}[/tex] into [tex]\text{Hz}[/tex].

[tex]2.70\,{\text{GHz=2}}{\text{.70}} \times {\text{1}}{{\text{0}}^9}\,{\text{Hz}}[/tex]

Substitute [tex]3.00 \times {10^8}\,{\text{m/s}}[/tex] for [tex]c[/tex] and [tex]2.70 \times {10^9}\,{\text{Hz}}[/tex] for [tex]f[/tex] in equation (1).

[tex]\begin{aligned}\lambda&=\frac{{3.00 \times {{10}^8}\,{\text{m/s}}}}{{2.70 \times {{10}^9}\,{\text{Hz}}}} \\&=0.11\,{\text{m}} \\&=1.1\times10^{8}\text{ nm} \\ \end{aligned}[/tex]

Thus, the wavelength of the microwave radiation produced by microwave oven is [tex]\boxed{1.1\times {10^8}\,{\text{nm}}}[/tex].

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Answer Details:

Grade: High school

Subject: Physics

Chapter: Electromagnetic radiation

Keywords:

Microwave oven, 2.70 GHz, 2.70 ghz, 2.70 times 10^9 Hz, wavelength, numerically, nanometers, 0.11 m, 0.11 times 10^9 nm, 1.1 times 10^8 nm , magnetron, 0.11 times 10power9 nm, 1.1 times 10 power 8 nm.